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Model-scale/full-scale correlation in open water and ice for Canadian
Coast Guard "R-Class" icebreakers
Spencer, D.; Jones, S. J.
https://publications-cnrc.canada.ca/fra/droits
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https://nrc-publications.canada.ca/eng/view/object/?id=0fe96263-ccea-4a63-868d-b8ff2135de56 https://publications-cnrc.canada.ca/fra/voir/objet/?id=0fe96263-ccea-4a63-868d-b8ff2135de56Journal of Ship Research, Vol. 45, No. 4, Dec. 2001, pp. 249–261
Journal of
Ship Research
Sir John Franklin, one of the R-Class icebreakers
Model-Scale/Full-Scale Correlation in Open Water and Ice
for Canadian Coast Guard “R-Class” Icebreakers
Don Spencer and Stephen J. Jones
National Research Council of Canada, Institute for Marine Dynamics, P.O. Box12093, Station A, St. John’s, Newfoundland A1B 3T5, Canada
Model-scale data from the National Research Council of Canada, Institute for Marine Dynamics’ water and ice towing tanks for the Canadian Coast Guard’s R-Class ice-breaker are compared with previous model tests and, more importantly, with three sets of full-scale ice trials data collected in 1978, 1979 and 1991. In open water, good agree-ment between model- and full-scale was found for bollard tests, and for self-propulsion tests provided a roughness allowance of 0.0008 was used. In ice, good correlation was found with the 1978 tests when the ship was new and there was little snow cover, using a model hull/ice friction coefficient of 0.05. Good agreement with the later tests, 1979 and 1991, was also obtained with somewhat higher model/ice friction coefficients of 0.055 and 0.065. This is attributed to a deteriorating, and hence rougher, full-scale ship hull surface. The model tests showed that a change in friction coefficient from 0.03 to 0.09 causes a doubling of the delivered power. For the full-scale ship, it is suggested that rel-atively inexpensive localized hull maintenance in the shoulder area, where ice jamming occurs and hence hull/ice friction is important, could improve performance and reduce the chance of structural damage.
Table 1 CCGS type 1200, R-Class, medium icebreaker L.O.A. 98.15 m L.B.P. 78.80 m Maximum breadth 19.5 m Draft 7.17 m Power 10,140 kW Drive AC/DC
Maximum speed 16.2 knot
Maximum RPM 180 Propellers 2 Number of blades 4 Diameter 4.115 m P/D (fixed pitch) 0.775 Rotation outboard Introduction
The Canadian Coast Guard operates three R-Class ice-breakers. They are the CCGS Sir John Franklin, Pierre Radisson, and Des Groseilliers. These vessels have a power of 10,000 kW and carry an Arctic Class 3 rating. Table 1 gives a summary of the general particulars for this ship class, and the frontispiece shows a picture of the ship.
This paper examines the correlation between R-Class ship tri-als in open water and in ice, with measurements on a 1/20-scale model tested at the Institute for Marine Dynamics, St. John’s, Canada. While the full-scale tests have been published in the lit-erature (Williams et al 1992, Edwards et al 1979), the model tests and the correlation have not, except for internal IMD reports. This ship is probably the most extensively tested icebreaker, having been the subject of a round-robin test program organized by the International Towing Tank Conference (Tatinclaux et al 1989).
Open water correlation included self-propulsion and bollard pull. Level ice resistance and power were correlated using the concept of “correlation friction” analogous to the correlation allowance used in clearwater testing. Strictly speaking, ice-hull friction should scale as unity and the friction coefficient of the model should equal that of the full-scale ship. There have been a few attempts to measure the ice-hull friction coefficient at full
Nomenclature
Note: When not otherwise noted, subscript M refers to model, S to ship
g = acceleration due to gravity hi= ice thickness
k = form factor by Prohaska (1966) n = rate of revolution of shaft (rps) 1 − t = thrust deduction factor
= inverse advance coefficient = water density
i= density of ice
= difference in density between ice and water
f= flexural strength of ice
B = maximum beam of model CA= ship-hull roughness correlation
allowance
CB= coefficient of buoyancy resistance
CBR= coefficient of breaking resistance
CC= coefficient of clearing resistance
CF= nondimensional coefficient of frictional resistance CT= nondimensional coefficient of total resistance D = propeller diameter FD= tow force
Fh= Froude number based on ice
thickness
FN= Froude number based on ship
length J = advance coefficient
JBOLL= nondimensional bollard advance
coefficient
KFD= nondimensional tow force
coefficient (equation 3) KQ= nondimensional torque coefficient
KT= nondimensional thrust coefficient
PD= delivered power
RB= buoyancy resistance due to ice
RBR= breaking resistance due to ice
RC= clearing resistance due to ice
RI= total ice resistance (excludes open
water) RN= Reynold’s number
ROW= open water resistance
RPS= pre-sawn resistance
RT= total resistance
S = wetted area
SN= strength number (equation 18)
T = maximum draft of model TI= thrust due to ice
TM= total thrust (port + starboard)
TOW= open water thrust
TTOT= total thrust
V = velocity of ship or model
scale (Mäkinen et al 1994, Schwarz 1986) and results have shown a very wide range of values from 0.01 to 0.6. It would be unreal-istic, therefore, to pick a single value for model-scale tests based on such measurements. Therefore, most ice tanks test a model at two or more hull-ice friction coefficients, by painting the model with different paints, and the friction coefficient that gives the best correlation with full-scale data is found. This is called the “correlation friction” coefficient, and it can then be used for other models. Since hull condition and snow cover dramatically influ-ence the hull-ice friction, only measurements on smooth hulls operating in relatively snow free conditions were considered for correlation purposes. In this paper, a correlation between full-scale and model full-scale tests in ice is shown in the following man-ner. First, full-scale open water bollard and speed-power trials are compared with corresponding model tests, from which it is shown that the model tests accurately predict the ship performance in open water, and a thrust deduction factor is determined from open water, overload, model tests. In general, a ship moving through an ice sheet is in an overload condition with the additional thrust overcoming the resistance of the ice. Thus, the thrust deduction factor used to estimate level ice resistance should be derived from overload tests. While it would be preferable to measure the thrust deduction factor at full-scale, these tests are expensive to conduct because they require a second vessel to provide a tow load. An alternative, therefore, is to use thrust deduction factors derived from model overload tests. Then, we argue that because open water self-propulsion and bollard pull may be considered extreme overload conditions, that is zero pull and maximum pull, respec-tively, if the model tests can predict ship performance for these conditions, it is likely that the model overloads will be valid gen-erally for the full-scale ship. Second, the full-scale trials in ice are discussed and the results summarized. Third, the model-scale resistance tests in ice are described and equations for the resis-tance of the full-scale ship derived from analysis of the model test results. Fourth, the full-scale resistance in ice for the ship is then determined from the measured trials data and the thrust deduc-tion factor mendeduc-tioned above, and it is shown that the equadeduc-tion from the model tests is a good fit to the full-scale data when the friction of the ship’s hull is considered. For one set of full-scale trials, delivered power was correlated, rather than resistance, by
estimating model power from model open water overload exper-iments and model level ice resistance.
Full-scale open water trials
The performance of the CCGS Sir John Franklin was measured in open water during the winter of 1990. Open water bollard pull experiments were conducted near Marystown, Newfoundland on January 23, 1990 (Spencer et al 1990a). Open water speed-power trials were conducted in Conception Bay, Newfoundland on February 1, 1990 (Spencer et al 1990b). Additional speed-power trial data were collected during acceleration trials con-ducted off St. John’s on May 24, 1991 (Williams 1991). A hull roughness survey was also conducted on the Sir John Franklin in December 1989.
Bollard tests
Bollard pull tests (Spencer et al 1990a) were conducted by connecting a 100-m-long, 3-in-diameter, wire rope from the bol-lard to the vessel aft towing winch. A 100 tonne clevis pin type dynamometer recorded the tow force. The winch manufacturer recommended that the towing force not exceed 66 tonnes so the maximum shaft speed was limited to 105 rpm (about half power). The water depth near the jetty was approximately 15 m, slightly greater than twice the vessel draft. Table 2 contains a summary of these test results. Shaft power was determined from torque and shaft revolutions; indicated power from amperage and voltage readings.
Open water propulsion tests
The open water tests in Conception Bay (Spencer et al 1990b) (Table 3) were run over a one mile course with, and against, the wind. The wind was initially 25 knots but fell during the trials to 13 knots. Seven shaft speeds were set from 170 to 60 rpm. The resulting ship speed was corrected for wind using the method
Table 2 Summary of bollard pull tests (Spencer et al 1990a)
Total Shaft Total Indicated
Shaft Speed, Total Thrust, Power, Power, Tow Rope Pull,
rpm kN kWkW kN 58 120 587 656 175!7 70 154 971 1062 234!0 79 330 1405 1547 336!9 88 417 2047 2219 416!5 94 453 2392 2577 450!4 99 502 2911 3128 520!3 104 548 3460 3717 593!2 98 506 2817 3021 515!5 94 479 2453 2640 465!0 90 441 2177 2336 431!0 80 328 1420 1538 314!5 70 246 959 1049 232!0 59 179 601 673 173!8 50 130 384 432 118!4 40 72 205 240 69!9 29 39 95 116 33!0
of Isherwood (1972). No correction for current was made. For the later test (Williams 1991) the ship had to run abeam of the wind to avoid icebergs and a 0.25 to 0.5 knot current was present. There were only five tests with shaft speeds of about 180 rpm. Corrections were made for current but not wind.
Hull roughness survey
A hull roughness survey was conducted on the CCGS Sir John Franklinwhile it was in drydock at Halifax Industries Ltd. on 1 December 1989 (Spencer et al 1990b). The survey used a BSRA hull roughness analyzer Mk IIa. The instrument displays the max-imum peak to valley height over a 50 mm segment of the hull.
The overall mean hull peak-valley roughness from 90 locations was 316 "m. It varied from a mean of 364 "m over the starboard bottom to 277 "m on the port side. In general, the hull was rough by modern standards. A legacy of blasting and touching-up was evident and many textures were evident. Further details can be found in Spencer et al (1990b).
Model open water tests
All model open water experiments were conducted in IMD’s 200-m long clearwater towing tank.
Bollard pull
A 1:20 scale model was outfitted with scale propellers. The model had a glossy finish and could be considered hydraulically smooth. Turbulence was stimulated by 5 mm diameter trip wires placed 5% of LBP aft of the bow profile.
Two bollard pull experiments were conducted with the towline connected to the stern at an elevation corresponding to the aft towing winch. First, the model was tested in the center of the towing tank simulating deep water, and then it was tested with the
Table 3 Summary of open water self-propulsion trials (Spencer et al 1990b)
Total Shaft Total Indicated Shaft Speed, Ship Speed, Total Thrust, Power, Power,
rpm knots kN kWkW 57 5!9 42 254 300 57 6!3 49 295 322 79 8!2 88 601 689 77 8!3 95 650 695 98 10!2 136 1153 1207 98 10!8 150 1281 1268 120 12!3 214 2109 2230 120 12!4 225 2186 2293 135 13!7 300 3210 3367 135 13!7 283 3061 3272 150 14!9 386 4450 4660 150 15!0 371 4304 4557 186 16!05 729 9879 10258 174 16!1 597 7108 7928 174 16!2 612 7534 7976 183 16!45 699 9391 9661 184 16!55 714 9568 9924 185 16!75 741 9928 10258
0 100 200 300 400 500 600 700 800 0 1000 2000 3000 4000 5000
Total Shaft Power kW
Bollard Tow Force kN
Bollard tow force Predicted tow force
Fig. 1 Results of the Marystown bollard tests showing excellent cor-relation between full-scale data (diamonds) and predicted data from model tests (squares). The line is a third-order polynomial fit to model
data only
model close to a plywood mock-up of the pier at Cow Head to simulate the shallow water depth. The tests were conducted over the range of shaft speed covered in the full-scale trials. In addition to the above, one conventional bollard test was conducted with the tow point at the propeller shaft line, resulting in very little trim moment.
Analysis of bollard data
Analysis began with calculating and plotting the standard nondimensional coefficients of thrust KT, torque KQ, and tow
force KFD, against JBOLL, from the model data. JBOLL is defined
as n√D/g where D is the propeller diameter, n is the rate of rev-olution of the shaft (rps), and g is the gravity acceleration. KFDis
defined below in equation (3). Polynomials were fitted to smooth the data. Since no discernible difference was seen between the deep water and pier mock-up tests, the data were combined for subsequent analysis. The smoothed coefficients were used to com-pute thrust, torque and towing force for the ship at bollard condi-tion, using a sea water temperature of 3C and a salinity of 3%.
Figure 1 compares the towing force between the ship and model. Excellent agreement is seen in this figure between the smooth curves derived from the model tests, and the points from the full-scale tests. Similar agreement was found for propeller thrust and delivered power.
Resistance and self-propulsion
The model was outfitted as for the bollard pull tests with the towing load cell placed in the model at an elevation corresponding to the shaft line. The model drafts were altered to correspond to the full-scale speed-power trials (6.76 m fore and 7.24 m aft). Self-propulsion experiments were carried out using an overload technique. The model was tested at five speeds corresponding to ship speeds of 6, 9, 13, 15, and 17 knots. At each speed, propeller revolutions were varied to cover a range of power, from the ship self-propulsion point to full power.
Resistance tests were also conducted on the model and a form factor, 1 + k, was determined by the method of Prohaska (1966), and adopted by the ITTC. The two nondimensional coef-ficients for total resistance, CT, and for frictional resistance, CF,
were first calculated. CT is the total resistance coefficient of
the ship (subscript S) and model (subscript M ) and is given by CT= RT/0!5 SV2, where RT is the measured total resistance,
is the water density, S is the wetted area and V is the velocity. CFM and CFS were calculated from the ITTC (1957) ship model
correlation line
CF =
0!075 log10RN− 22
(1) where RN is the Reynold’s number for the ship or the model,
and FN is the Froude number. A plot of [(CTM/CFM)–1] against
(FN)4/CFM (Prohaska 1966), then resulted in the intercept, k =
0!4, or a form factor, 1 + k = 1!4.
The model self-propulsion data were reduced to the standard nondimensional coefficients KT$ KQ$ KFD and plotted against J ,
the advance coefficient. The ship self-propulsion point at each speed was determined by first plotting 2 against the
nondimen-sional towing force, KFD, where
= nDV = J−1 (2)
and
KFD=
FD
0!5 SV2 (3)
where FD is the tow force. From this graph, the ship
self-propulsion point was determined, and the value of 2, and hence
J , determined. Thus, the values of KT and KQ at the
self-propulsion point were determined. The resulting curves were interpolated at the difference in the model-ship resistance coeffi-cient, CTS-CTM:
CTS− CTM= 1 + kCFS− CFM − CA (4)
where CA is the ship hull roughness correlation allowance
(assumed zero for the model) and the ship hull roughness corre-lation allowance, CA, was varied from 0.0004 to 0.0008.
Predictions for the ship were based on a water temperature of 3C and a salinity of 3.5%. For each ship self-propulsion shaft
speed $ KT and KQwere determined. From these, thrust, torque,
and delivered power were calculated. Figure 2 shows the compar-ison of total shaft power predicted from the model tests and those measured on the ship. The agreement is good when a correlation allowance of 0.0008 is used. The acceleration tests conducted in May 1991 contained scatter in the speed measurements. This may have been due to the tests having been conducted across the prevailing wind, to avoid some icebergs, which may have led to excessive rudder angles being used to maintain course. Similar good correlation was found for thrust and shaft speed when a 0.0008 correlation allowance was used.
Model overload experiments
The model was outfitted as for the self-propulsion tests except the drafts were altered to correspond to the full-scale speed-power trials in ice (6.76 m fore and 7.24 m aft). The model was tested
0 4000 8000 12000
5 10 15 20
Ship Speed knot
Total Shaft Power kW
Full scale data FS acceleration trials MS data, Ca=0.0008 MS data, Ca=0.0004
Fig. 2 Open water total shaft power for ship and model data for two correlation allowances, showing a good exponential fit with an allowance of 0.0008 (sea water 35 ppt, temp. 2C, form factor 1 + k =
14). See text regarding the acceleration trials
at four speeds corresponding to ship speeds of 4, 7, 10, and 13 knots. At each speed, propeller revolutions were varied from 120 to 180 rpm, typical of those used in ship trials.
Overload analysis—Model overload thrust, torque and tow-ing force were also reduced to nondimensional coefficients and plotted against advance coefficient, J . These curves were then smoothed by fitting second-order polynomials. The thrust-deduction factor, (1 − t), was calculated for the model using
1 − t =FD+ RT TM
M
(5) where FD is the tow force, RTM is the open water resistance of
the model, and TM is the total thrust of the model (port plus
starboard). The total model resistance, RTM, was calculated by
interpolating the model resistance curve at the appropriate model speed. The model thrust, TM, and towing force, FD, were
calcu-lated from KT and KFD curves, respectively. In Fig. 3 the thrust
deduction factor from equation (5) is plotted as a function of the advance coefficient for these tests.
The total thrust for the full-scale ship was then calculated using a water temperature of 2C and a salinity of 0.5% (for water
density) which corresponded to values measured during full-scale icebreaking trials (Williams et al 1991, 1992). Ship open water resistance, RTS, was estimated from the model resistance using a
form factor of 1.4 and a correlation allowance of 0.0008. Ship tow line pull was calculated by multiplying total thrust by the model thrust deduction and subtracting ship open water resistance. Ship torque, and hence delivered power, was predicted using KQ
inter-polated from KQ versus J curves. In Fig. 4, tow force is plotted
against delivered power for the ship at 4, 7, 10, and 13 knots. To aid in interpolating at intermediate ship speed, a regression analysis was performed on these data resulting in
PD= C0+ C1FD+ C2FD2 (6)
where PD is the delivered power (kW) and FD is tow force
(kN). The coefficients are functions of ship speed (knot) and are
y = 0.463x2 - 0.137x + 0.129 R2 = 0.96 0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0 Advance Coefficient Js Thrust Deduction t d
Fig. 3 Thrust deduction factor from equation (5) is plotted as a function of the advance coefficient. The line is a second-order
polynomial fit
given by
C0 = −2099 + 191 VS+ 13!8 VS2 (6a)
C1 = 10!0 − 0!608 VS+ 0!053 VS2 (6b)
C2 = 0!00146 + 0!000237 VS (6c)
Full-scale level ice trials
Several full-scale speed-power icebreaking trials have been conducted with this ship class. The CCGS Pierre Radisson was tested soon after delivery in 1978 during transit in the Central Arctic, and in February of 1979 further tests were conducted in thinner but stronger ice in the St. Lawrence River (Edwards et al
-200 0 200 400 600 800 1000 1200 1400 0 5000 10000 15000
Total Shaft Power kW
Tow Force kN
4 knot 7 knot 10 knot 13 knot
Fig. 4 Predicted towing force plotted against delivered power for ship 4, 7, 10, and 13 knots from overload tests
Table 4 Summary of full-scale ice trials for CCGS Pierre Radisson, 1978 (Edwards et al 1979)
Shaft Ship Ice Ice Total Ice Shaft Revs., Speed, Thick., Strength, Thrust, Thrust, Power,
rpm m/s m kPa kN kN kW 160 2!30 1!17 208 1120 1097 9938 141 2!78 1!05 208 965 930 6894 133 2!57 0!93 208 769 740 5829 119 1!90 1!16 208 707 691 4233 111 1!34 1!03 208 622 614 3506 102 0!87 0!95 208 500 496 2524 162 3!61 1!02 208 1077 1014 10928 141 2!72 1!02 208 876 844 6922 126 2!21 0!93 208 749 728 4863 109 1!13 1!04 208 557 550 3137 99 0!41 0!98 208 487 485 2533 112 1!70 0!95 208 535 522 3577 162 3!33 1!17 208 1091 1039 9957 117 1!34 1!02 208 631 623 3891 156 3!91 0!96 208 928 853 11060 136 1!48 1!17 208 1024 1014 6931 122 1!49 0!98 208 663 653 4376 140 3!29 0!98 208 858 806 7729 133 1!25 1!17 208 877 868 6136 131 1!75 1!03 208 771 756 5327 136 2!71 1!03 208 836 804 6414 121 1!11 1!17 208 715 708 4345 122 1!99 1!07 208 631 614 4688 143 2!21 1!07 208 875 854 7191 162 3!50 1!03 208 1167 1108 10213 161 3!70 1!0 208 1184 1117 10534 161 3!96 1!12 208 1200 1122 10352
1979). Two probes were made by CCGS Sir John Franklin into Lake Melville in 1980 (Michailidis 1980). Finally, in February 1991, further tests were conducted on this ship in Notre Dame Bay, Newfoundland (Williams et al 1991, 1992).
The July/August 1978 trials were conducted during a partial transit through the Northwest Passage. Ice thickness was in the range 0.8 to 1.3 m. Ice flexural strength was estimated to be about 200 kPa. Table 4 contains a summary of these trial data. Table 5 gives a summary of the February 1979 trials performed in ice with a thickness ranging from about 0.2 to 0.7 m. Only the snow-free data are included. Ice flexural strength varied from 400 to 500 kPa as determined by cantilever beam tests. During the first probe into Lake Melville in January 1980, the ice thickness was about 0.65 m. During the second probe in March of that year the ice thickness was about 0.8m. Flexural strength was estimated to be about 300 kPa. During both of these Lake Melville trials there was significant snow cover, so these trials were not included in this correlation study.
Table 6 contains a summary of the snow free data from the February 1991 trials where ice thickness was between 0.5 and 0.6 m. Thrust was measured from the hydraulic pressure on a Mitchell thrust bearing. The ice had a flexural strength between 200 and 300 kPa determined from beam tests. Together these trials constitute a large body of data describing the performance in ice for this hull form.
Table 5 CCGS Pierre Radisson trials of February 1979 no snow (Edwards et al 1979)
Ship Ice Ice Ice Total
Speed, Thickness, Strength, Thrust, Thrust, Power,
m/s m kPa kN kN kW 1.75 0!200 407 126 111 · · · 2.31 0!210 407 138 115 · · · 1.85 0!230 407 174 158 · · · 1.94 0!230 407 178 162 · · · 2.71 0!230 407 237 205 · · · 2.92 0!230 407 301 263 · · · 3.82 0!230 407 335 264 · · · 4.98 0!230 407 387 267 · · · 5.81 0!230 407 520 350 · · · 5.81 0!230 407 549 379 · · · 6.99 0!230 407 631 348 · · · 3.13 0!250 407 194 150 · · · 2.00 0!337 407 151 133 · · · 1.11 0!350 407 180 174 · · · 3.13 0!350 407 342 298 · · · 6.99 0!350 407 864 581 · · · 3.82 0!433 407 449 378 5450 2.15 0!435 407 381 360 2365 3.13 0!446 407 519 474 4027 1.44 0!463 407 276 267 2163 1.74 0!482 407 345 331 2451 3.75 0!480 407 595 524 3353 5.76 0!480 407 931 760 8888 6.27 0!480 407 918 705 8365 3.62 0!678 524 932 869 8301 1.05 0!693 524 436 429 2213 4.10 0!693 524 1019 937 9775 1.33 0!698 524 500 492 3373 3.07 0!709 524 751 707 · · · 1.61 0!724 524 479 467 · · · 2.42 0!716 524 638 613 · · · 3.13 0!718 524 831 786 6134 3.83 0!719 524 949 878 7432
Model level ice resistance
The object of this section is to derive equations for the level ice resistance from the model tests, which can later be used to predict the resistance of the full-scale ship. Model level ice resistance
Table 6 Summary of full-scale trials of Sir John Franklin, February 1991 (Williams et al 1991)
Shaft Ice Ice Shaft Indicated Revs., Ship Speed, Thickness, Strength, Thrust Power, Power,
rpm m/s m kPa kN kWkW 139 4.7 0.49 193 618!9 5315 5715 115 3.2 0.50 265 478 3280 3484 151 4.9 0.50 265 755!3 6908 7361 139 5.0 0.53 0 582!7 5139 5511 169 6.3 0.53 193 857!5 9316 10134 148 4.6 0.56 274 768!7 6852 7277 109 2.3 0.59 274 484!1 3000 3237 167 5.6 0.60 274 955!9 9811 10516
tests cover a wide range of speed, ice thickness and strength as well as two hull-ice friction coefficients. Model test data for this study come from two sources; the original data from tests on a 1:20 scale model with a 0.09 friction coefficient (Newbury 1988), called the high friction model, and more recent tests conducted on the same model with a hull-ice friction of 0.03 (Spencer et al 1992b), called the low friction model. We follow the IMD stan-dard method of analysis (IMD Stanstan-dard Test Method 2000) which involves dividing the total ice resistance, RT, into four
compo-nents; open water, ROW, ice buoyancy, RB, ice clearing, RC, and
ice breaking, RBR
RT= ROW+ RB+ RC+ RBR (7)
In addition to the usual level ice resistance the model was also towed in ice which was pre-broken or pre-sawn to remove the breaking component, RBR, thus
RPS= ROW+ RB+ RC (8)
Open water
Open water resistance tests were conducted in the clearwa-ter towing tank for the low friction model only. It was assumed that the open water resistance was the same for the high fric-tion model. For model velocity, VM, less than 1.0 m/s (9 knot
full-scale), the results fitted the equation
ROW = 14!6 VM2 (9)
with a correlation coefficient of 0.999, as shown in Fig. 5. ROW
is measured in Newtons and VM in m/s. The open water
resis-tance was subtracted from the pre-sawn ice resisresis-tance yielding a total ice clearing term, RB+ RC. This consists of a buoyancy
component, RB, which is assumed independent of speed, and a
component that is speed dependent, RC. It is assumed that at low
or creeping speeds (i.e., 0.02 m/s), the only resistance remain-ing will be due to ice buoyancy and hence RC goes to zero at
y = 14.60x R2 = 1.00 0 2 4 6 8 10 12 14 0 0.2 0.4 0.6 0.8 1
Model Speed Squared (m/s)2
Resistance N
Fig. 5 Open water resistance for R-Class model 327. Low friction model was tested and results assumed to be the same for high
friction model
low speed. Figure 6 shows (RB+ RC) plotted against VM. The
intercept at VM equal to zero gives RB.
Ice buoyancy
Figure 7 shows RBplotted against the buoyancy of the ice given
by ghiBT , where is the difference in density between ice
and water, g is gravity, hiis the ice thickness, B is the maximum
beam of the model, and T is the maximum draft of the model. From Fig. 7, a nondimensional coefficient of buoyancy resistance, CB, is given by the slope of the best fit line through the origin,
since it is assumed that when the buoyancy is zero, the buoyancy resistance must also be zero
RB= RPSV →0= CB ghiBT (10) y = 25.76x + 15.70 y = 18.79x + 8.80 y = 12.51x + 4.15 0 5 10 15 20 25 30 35 0.0 0.2 0.4 0.6 0.8 1.0 Model Speed m/s RB + R C N 22 mm 35.4 mm 50 mm (a) (b) y = 22.10x + 10.99 y = 37.37x + 17.40 y = 60.17x + 31.50 0 10 20 30 40 50 60 70 80 90 100 0 0.2 0.4 0.6 0.8 1 Model Speed m/s RB + R C N 22 mm 35.4 mm 50 mm
Fig. 6 Plot of pre-sawn resistance minus open water, RB+ RC, for
one ice density 940 kg/m3, for R-Class model 327; (a) for low friction
y = 1.31x R2 = 0.88 y = 2.67x R2 = 0.92 0 5 10 15 20 25 30 35 0 5 10 15 Buoyancy N RB N
High friction Low friction
Fig. 7 Creeping speed buoyancy resistance, Rb, plotted against
cal-culated ice buoyancy for three ice thicknesses. Slope of the line through the origin gives buoyancy coefficient Cb
From the slope of the lines in Fig. 7, CBwas found to be 2.67 for
the high friction model (" = 0!09) and 1.31 for the low friction model (" = 0!03). The difference was assumed to be due to the relative motion between the hull and ice (Spencer et al 1992b). Ice clearing
The buoyancy resistance, equation (10), and the open water resistance, equation (9), were then subtracted from the pre-sawn resistance to give a net speed dependent, clearing resistance, RC
RC= RPS− ROW− RB (11)
This resistance is made nondimensional by dividing by iBhiVM2
so that
CC=
RC
iBhiVM2
(12) where CC is the coefficient of the clearing resistance, and i is
the density of the ice.
Model speed was made dimensionless by using a Froude num-ber, Fh, where the ice thickness is the characteristic length
Fh=
VM
ghi
(13) In Fig. 8, the clearing coefficient is plotted against this thickness Froude number on a ln-ln scale. Linear regression of the data yielded
RC = 0!900Fh−0!739 iBhiVM2 (14)
RC = 2!03Fh−0!971 iBhiVM2 (15)
for the low and high friction models, respectively.
y = -0.971x + 0.71 R2 = 0.96 y = -0.739x - 0.11 R2 = 0.89 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 ln Fh ln C C
High friction Low friction
Fig. 8 A ln-ln plot of clearing coefficient against Froude number for R-Class model 327
The pre-sawn resistance can now be calculated from tion (8) using expressions for the open water resistance of equa-tion (9), the buoyancy resistance of equaequa-tion (10), and the clearing resistance of equation (14) or (15).
Breaking resistance
The breaking resistance of the model cannot be measured directly but was determined by subtracting the pre-sawn resis-tance from the total level ice resisresis-tance
RBR= RT− RPS (16)
The breaking resistance was also nondimensionalized by dividing by iBhiVM2
CBR=
RBR
iBhiVM2
(17) In Fig. 9, this breaking coefficient, CBR, is plotted against a
nondi-mensional strength number, SN, defined as
SN = VM fhi iB (18)
where f is the flexural strength of the ice.
These curves are linear on a log-log basis and linear regression yields the following expressions for the low and high friction models, respectively.
CBR= 1!08 SN−1!672 (19)
CBR= 2!19 SN−1!579 (20)
The above equations can now be summed together to give the total ice resistance, RI, for the model. The open water resistance
y = -1.579x + 0.783 R2 = 0.96 y = -1.672x + 0.076 R2 = 0.97 0.0 1.0 2.0 3.0 4.0 5.0 -3.0 -2.0 -1.0 0.0 1.0 ln SN ln C BR
High friction Low friction
Fig. 9 A ln-ln plot of breaking coefficient against strength number for R-Class model 327
can also be added if required: RI = 0!90 Fh−0!739 iBhiV 2 M+ 1!08 SN−1!672 iBhiV 2 M +1!31 ghiBT (21) RI = 2!03 Fh−0!971 iBhiV 2 M+ 2!19 SN−1!579 iBhiV 2 M +2!67 ghiBT (22)
Equations (21) and (22) give the total level ice resistance for the low and high friction model, respectively. Figure 10 shows that these equations do indeed describe well the model data, which it should be since the equation was derived from the data, but it acts as a check on the above manipulations. At high
0 50 100 150 200 250 0 50 100 150 200 250
Measured total resistance N
Calculated total resistance N
High friction Low friction
Fig. 10 Comparison of calculated total resistance from equation (22) and experimentally measured values. Dotted line is a 1:1 fit and shows
that equations (21) and (22) do indeed describe the data well
0 40 80 120 160 200 0 0.2 0.4 0.6 0.8 1 Model speed m/s Resistance N Rb Rc Rtot. Rbr Row
Fig. 11 Components of total resistance in ice for high friction model, for ice between 22 and 38 mm thick, and 43-63 kPa flexural strength
resistance the fit is not so good, but these conditions are well outside the full-scale operational range of the ship and so this is not significant.
These equations (21) and (22), which were derived entirely from model tests, can now be used to give the resistance of the full-scale ship at the conditions of the full-scale trials.
Relative magnitude of components
The relative magnitude of the components is shown in Fig. 11 for the case of the high friction model and ice data of 33–38 mm thickness, and 43 to 63 kPa flexural strength. It can be seen that at a model speed of 0.5 m/s (full-scale 4.5 kn.) the icebreaking term (92 N) is 67% of the total (137 N). The buoyancy and clearing terms are both about 15% and the open water term is only 3%. These values compare with model data of Poznak & Ionov (1981) who showed that for a “medium size icebreaker” the breaking term was about 40% of the total, somewhat smaller than our value. However, Enkvist (1983) has estimated that the breaking term in full-scale is between 40–80% of the total resistance, with the larger figure applying to smaller ships. Our value of 67%, therefore, seems quite reasonable.
Comparison with previous R-Class model data
As mentioned in the introduction, the R-Class model was the subject of an ITTC round robin test series (Tatinclaux et al 1989). They analyzed their data differently but for comparison we have plotted RT/ gBh2i against Fh in the same way as they did, as
shown in Fig. 12. The points on this graph are ours, but the line is the mean regression equation from Tatinclaux et al (1989) for their smooth model (Table 6, p. 36, All labs, Form I). Our data fall slightly below their mean curve, but the agreement is good considering the scatter in their data from the different laboratories.
Correlation between model and ship in level ice The correlation was by comparing measured ship resistance, and predicted ship resistance from equations (21) and (22), for the
Line is equation fitted to ITTC data 0 2 4 6 8 10 12 0.0 0.5 1.0 1.5 2.0 Fh RT /ro.g.B.h i 2
Fig. 12 Comparison of present data shown as the points, with the mean regression line obtained by Tatinclaux et al (1989), in their ITTC
round robin tests series
three trials, and also by a comparison of measured and predicted delivered power for the 1979 trials. For the 1979 trials, the shaft speed was not reported and so an advance coefficient, and hence a thrust deduction factor, could not be calculated from Fig. 3. Instead it was assumed constant at the mean value found in the 1991 trials (0.164), and resistance during the trials was calculated using this value. An additional comparison of delivered power was made, therefore, for the 1979 trials.
Ship resistance
First, we calculated the resistance in ice for the full-scale ship from the trials data. The thrust required in ice, TI, first calculated
by subtracting the open water thrust, TOW, from total ship thrust,
TTOT, measured in ice, both of which were measured on the trials:
TI= TTOT− TOW (23)
The resistance in ice, RIS, for the ship was estimated by
multi-plying the ice thrust by a thrust deduction factor derived from the above model overload tests, shown in Fig. 3:
RIS= 1 − tTI (24)
This was then compared with the ice resistance from the model tests given by equations (21) and (22) above.
Model delivered power
Model self-propulsion tests in ice were not performed so deliv-ered power for the model had to be estimated from the model ice resistance tests and the performance of the model in overload conditions in open water. In other words, the model ice resistance was equated to the tow force in overload tests in open water, and then the delivered power was calculated from the overload results
discussed above. In doing this, three assumptions are made: 1. ship performance is well represented by model overload
results,
2. wake and thrust deduction are not influenced by hull-ice interaction, and
3. the level of propeller ice interaction is not significant. The first assumption is justified by the good correlation of the ship and model in self-propulsion and bollard pull. The sec-ond is justified because full-scale data (Gagnon & Spencer 1991) indicate that thrust deduction is not significantly altered by the presence of ice. Thirdly, ship trials aboard the CCGS Sir John Franklin(Williams et al 1991) indicated that the level of propeller ice interaction in ice up to 0.6 m was not significant. However, it is expected that during the summer Arctic trials in ice up to 1.2 m thick, some ice propeller interaction would have been present. Since the model results do not account for this they may be assumed optimistic, that is, the power predicted may be slightly low.
Using the ice properties and ship speed presented in Tables 4 to 6, strength numbers and thickness Froude numbers were com-puted for the trial conditions. These were substituted in equa-tions (21) and (22) to compute the ice resistance for the model at both friction coefficients. Model delivered power was then esti-mated by letting this ice resistance equal the open water tow force in equation (6).
Correlation results
Figures 13, 14, and 15 show the ice resistance for the full-scale ship as calculated from the model tests by equations (21) and (22), against that estimated from the full-scale ship trials. Figure 13 is for the Arctic 1978 trials of the Pierre Radisson,
1:1 Fit High friction (0.09) y = 1.56x Low friction (0.03) y = 0.75x 0 400 800 1200 1600 2000 0 200 400 600 800 1000
Resistance from trials kN
Resistance from eqn. 21 & 22 kN
Fig. 13 Comparison for CCGS Pierre Radisson during August 1978 trials. Data points are calculated from equations (21) and (22) for con-ditions corresponding to full-scale trials. The line of perfect correlation (1:1) lies approximately midway between high (0.09) and low (0.03)
friction model test results, implying a perfect correlation of 0.05
1:1 fit Low friction (0.03) y = 0.70x High friction (0.09) y = 1.41x 0 200 400 600 800 1000 0 200 400 600 800 1000
Resistance from trials kN
Resistance from eqn. 21 & 22 kN
Fig. 14 Comparison of ship resistance for CCGS Pierre Radisson dur-ing February 1979 trials, with resistance calculated from model
equa-tions (21) and (22), implying a perfect correlation friction of 0.055
Fig. 14 for the February 1979 trials of the Radisson and Fig. 15 is for the 1991 trials of the Franklin. For these figures, the line of perfect correlation clearly lies between the two model friction coefficients of 0.03 and 0.09. If it is assumed that the influence of friction on resistance is linear over this range, an estimate of the “perfect correlation friction” may be obtained from these figures. From Fig. 13, it is estimated that the perfect correlation friction is 0.05 for the 1978 Arctic CCGS Pierre Radisson trials. Figure 14 shows a perfect correlation of 0.055 for the St. Lawrence trials of the Radisson in February 1979.
1:1 fit Low friction (0.03) y = 0.62x High friction (0.09) y = 1.25x 0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 700
Resistance from trials kN
Resistance from eqn. 21 & 22 kN
Fig. 15 Results for Sir John Franklin trials in Notre Dame Bay in February 1991. The 0.09 friction model results are only about 15% high,
implying a perfect correlation friction of 0.065
Finally, in Fig. 15 results are presented for the February 1991 trials of the Franklin in Notre Dame Bay. In this case, it appears that the 0.09 friction model results are only about 15% high, resulting in a perfect correlation friction of 0.065.
For Figs. 13 and 15, the thrust deductions were calculated from Fig. 3 above because the advance coefficient could be calculated from the data given. For the February 1979 trials (Fig. 13), the advance coefficient was not reported so the thrust deduction could not be calculated from Fig. 3 above. It was assumed constant at 0.164, the mean value obtained in the 1991 Franklin trials. However, shaft power was reported for some of the trials. Because of this, a second correlation based on model delivered power, as described in the preceding section, was used for the February 1979 trials data, and the result shown in Fig. 16. The perfect correlation line implies a value of 0.06, slightly higher than that in Fig. 14.
Error analysis
It is difficult to estimate all our errors for two main reasons. First the full-scale data were collected by different organizations and no estimate of errors was given in their reports. Second, the model data were all collected at IMD but on several differ-ent occasions, and again no estimates are given in the reports. However, based on experience we can say the following. The sys-tematic errors are small since all instrumentation was calibrated against standard values and could be read to more than suffi-cient decimal places. The chief source of random errors is the variation in the ice properties both at full-scale and model scale. At full-scale only a few ice thickness measurements are usually made for a given “run” and the mean is used as the true thick-ness. From experience, this gives an error of about ±10%. The flexural strength is usually estimated from core measurements of salinity, temperature and density. They have an error of at least ±20%. In the ice tank the errors are smaller because more mea-surements are taken and the environmental conditions are more uniform. We normally find a standard deviation for ice thickness
1:1 Fit High friction (0.09) y = 1.42x Low friction (0.03) y = 0.64x 0 2000 4000 6000 8000 10000 12000 14000 0 2000 4000 6000 8000 10000
Power from Ship Trials kW
Power from Model Tests kW
Fig. 16 Comparison of delivered power for the CCGS Pierre Radisson during February 1979 St. Lawrence trials, implying a perfect correlation
of ±3%, and for strength ±10%. The combined effect of these errors is to give an error in model resistance of ±8%. We esti-mate, less confidently, that the error in full-scale resistance would be ±15%. These error bars are shown as an example in Fig. 15. These errors do not affect the overall conclusions of this research but illustrate the degree of confidence in the model and full-scale tests. This also illustrates the importance of the ice measurements in the overall accuracy of full-scale and model scale tests.
Conclusions and discussion
1. For the bollard pull tests, a good correlation existed between model and ship. The model tests predicted accurately the bol-lard pull, thrust and power.
2. The model self-propulsion open water tests also correlated well with the ship if a roughness allowance of approximately 0.0008 was used. This is close to the value of 0.0009 which is obtained by Bowden & Davison’s (1974) method, for a hull with a surface roughness of 316 "m, but somewhat higher than the 0.0005 given by Holtrop & Mennen’s (1978) equation. 3. The ice resistance model tests agreed reasonably well with
the previous ITTC round-robin series of tests. The icebreaking component of the resistance was shown to be 67% of the total resistance at 0.5 m/s.
4. Models with a hull-ice dynamic friction of 0.05 gave good correlation for a new R-Class hull in snow-free ice, as was the case for the 1978 trials. The winter 1979 St. Lawrence trials required a slightly higher coefficient, between 0.055 and 0.06, but this may be due at least partially to a deteriorating hull condition. This relatively small change in correlation fric-tion between the 1978 and 1979 trials demonstrated that the model tests predicted ship performance over a wide range of ice conditions. For the trials in 1991, a higher model hull-ice friction coefficient of about 0.065 was required. We believe that this is because the hull, although coated with INERTA, was rough due to poor paint application and the condition of the underlying hull. These results point to a gradual decline in hull condition over the 13-year period. It is worth noting that Enkvist & Mustamaki (1996) also found good model to full-scale correlation for the Protector with a friction coefficient of 0.05.
5. The model tests demonstrated that there was almost a doubling of delivered power when going from a hull-ice friction of 0.03 to 0.09. This is shown by the slope of the correlation lines in Figs. 13–15 that double between the two friction values. Even if a hull-ice friction of 0.05 represents the best finish that can be achieved on a new hull, there appears to be almost a 50% increase in required power if it is allowed to deteriorate to a 0.09 finish. This represents a 10% increase in power for every 0.01 change in friction coefficient.
6. The R-Class hull form may be sensitive to friction because of the jamming of ice near the shoulders. As the broken ice cusps rotate normal to the hull they become jammed between the hull and the intact ice sheet. This jamming occurs only near the shoulders where the beam is approaching its maximum. Since the flare angles can be steep, in excess of 80 deg, hull ice friction can play a significant role in inducing jamming. Consider Fig. 17 which shows an ice floe trapped between the hull and intact ice sheet. The hull is exerting a normal force,
Fig. 17 Diagram to illustrate an ice floe trapped between hull and intact ice sheet
N on the floe, giving rise to a frictional force "N opposing motion. The hull then exerts a downward or clearing force on the ice piece of
F = N sin % − " cos % (25) where % is the angle of the hull segment measured relative to the vertical. It can be seen from equation (25) that if " becomes equal to tan % then there is no net clearing force and failure must occur by means other than flexure, typically crushing. The result would be very high local loads, leading to increased resistance and the possibility of structural dam-age. For example, if the hull-ice friction is 0.1, then a local flare angle of 84 deg or greater results in the ice becoming jammed regardless of normal load. For a hull-ice friction of 0.2, the critical flare angle is reduced to 79 deg. It is possible, therefore, that inexpensive localized hull maintenance in this shoulder region would greatly improve the performance of the ship and reduce the chance of structural damage.
Acknowledgments
We are grateful to all at IMD, too numerous to mention, who have conducted model tests and full-scale trials over the past 17 years. We are also grateful to Transport Canada and the Canadian Coast Guard for continued support, and to two anonymous refer-ees whose comments improved the paper.
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